[en] Design studies for the cooling channel of a Muon Collider call for straight and helical solenoids generating field well in excess of the critical fields of state of the art Low Temperature Superconductors (LTS) such as Nb₃Sn or NbTi. Therefore, High Temperature Superconductors (HTS) will need to be used for the manufacturing of all or certain sections of such magnets to be able to generate and withstand the field levels at the cryogenic temperatures required by the new machine. In this work, two major High Temperature Superconductors - Bi2212 round wires and YBCO coated conductor tapes - are investigated to understand how critical current density of such conductors scales as a function of external field and operating temperature. This is vital information to make conductor choices depending on the application and to proceed with the design of such magnets.